A new study on some Vandermonde matrices and systems

Abstract

In this paper, we first introduce a new concept on matrices which we call annihilator vectors. Then using the shifted form of these vectors, we propose new algorithms for (1) computing the inverse of a Vandermonde matrix, (2) solving some Vandermonde systems of linear equations, both algorithms in O(n 2) arithmetic operations. Our methods are based on a new technique which lead to novel algorithms, need less storage and, from experimental results, are more efficient than the previous usual methods. Finally, comparisons with other methods are broached and some numerical examples are supplied.